Journal of Advanced Research (2014) 5, 569–576

Cairo University

Journal of Advanced Research

ORIGINAL ARTICLE

Risk assessment of desert pollution
on composite high voltage insulators
Mohammed El-Shahat, Hussein Anis

*

Electrical Power Department, Faculty of Engineering, Cairo University, Giza, Egypt

A R T I C L E

I N F O

Article history:
Received 24 May 2013
Received in revised form 3 July 2013
Accepted 17 July 2013
Available online 24 July 2013
Keywords:
Composite insulators
Desert pollution
Power Lines
Insulator leakage current

A B S T R A C T
Transmission lines located in the desert are subjected to desert climate, one of whose features is
sandstorms. With long accumulation of sand and with the advent of moisture from rain, ambient humidity and dew, a conductive layer forms and the subsequent leakage current may lead to
surface discharge, which may shorten the insulator life or lead to flashover thus interrupting the
power supply. Strategically erected power lines in the Egyptian Sinai desert are typically subject
to such a risk, where sandstorms are known to be common especially in the spring. In view of
the very high cost of insulator cleaning operation, composite (silicon rubber) insulators are
nominated to replace ceramic insulators on transmission lines in Sinai. This paper examines
the flow of leakage current on sand-polluted composite insulators, which in turn enables a risk
assessment of insulator failure. The study uses realistic data compiled and reported in an earlier
research project about Sinai, which primarily included grain sizes of polluting sand as well as
their salinity content. The paper also uses as a case study an ABB-designed composite insulator.
A three-dimensional finite element technique is used to simulate the insulator and seek the
potential and electric field distribution as well as the resulting leakage current flow on its polluted surface. A novel method is used to derive the probabilistic features of the insulator’s leakage current, which in turn enables a risk assessment of insulator failure. This study is expected
to help in critically assessing – and thus justifying – the use of this type of insulators in Sinai and
similar critical areas.
ª 2013 Production and hosting by Elsevier B.V. on behalf of Cairo University.

Introduction
Leakage current on polluted insulators’ surface is a major cause
of insulation failure in high voltage power lines. Maintenance
of those lines thus necessitates the periodic cleaning the insulators’ surfaces, which is known to be a costly operation. The
* Corresponding author. Tel.: +20 1223121040; fax: +20 235723486.
E-mail address: (H. Anis).
Peer review under responsibility of Cairo University.

Production and hosting by Elsevier

magnitude of leakage current on a polluted insulator depends
on pollution severity and the contamination salinity, which

subsequently affects the conductivity of the contamination
layer. With thousands of kilometers of transmission and subtransmission lines in Sinai, rather than relying on the costly
insulator washing, composite insulators are nominated to be
used instead of ceramic insulators. Composite insulators are
now widely used worldwide because of their lower weight, higher mechanical strength, higher design flexibility, and their reduced maintenance. They display lower leakage current due
to their higher surface resistance [1,2]. Silicone rubber – used
to fabricate insulators – can provide long-term and satisfactory
service even under polluted and wet conditions. This is due to
its long-term hydrophobic surface properties. The hydrophobic

2090-1232 ª 2013 Production and hosting by Elsevier B.V. on behalf of Cairo University.
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570
surface inhibits the formation of a continuous water film and
the flow of leakage current along the surface. This blocks the
initiation of dry band arcing that leads to flashover. In a study
by Zhang and Hackam, the strong relation between hydrophobicity and high surface was established when high temperature
vulcanized (HTV) silicone rubber rods were subjected – under
high voltage – to accelerated wetting in salt-fog and immersion
in a saline solution [3]. The surface resistance was measured and
found to depend on the duration of the exposure to the salt-fog
without electric stress, the duration of the exposure to combined salt-fog and electric stress, and the specimen length.
The pollution layer accumulated on the insulator surface
during normal desert atmospheric weather has a thickness that
depends on the type of soil in this region and on the polluting
sand grain sizes. When sand is deposited on insulator surface
and in the presence of a major source of wetting, such as
dew in the early morning, leakage current would flow on the
surface. Conductive sand areas are then heated, and dry bands

are formed leading to possible surface flashover [4].
Relevant previous work in this area included estimating the
current density distributions along polluted insulator surface,
using surface charges simulation method [5]. Other studies simulated the leakage current while accounting for amount of salt
in the contamination layer [6]. Other experimental studies were
made on the effect of desert pollution on polymeric insulator
[7,8]. In another study, leakage current was estimated using
the FEMLAB software with different conductivities of contamination layer [9].
This paper aims to investigate the prime factor responsible
for initiating insulator failure under power-frequency voltage,
namely leakage current flowing through surface pollution.
Insulator simulation was carried out using an accurate 3-D
ANSYS software program, which is based on the Finite Elements method. The program required higher performance computing and gave results with high accuracy. The ratings of
transmission lines in Sinai are mainly 500 kV, 220 kV, and
66 kV. A typical two-shed insulator, which may be used on
220 kV power lines is used as a case study. Such leakage current
distributions are determined with different sand grain thickness
and with different sand conductivities. Realistic data are used,
which are based on sand samples collected from Sinai desert
near present and future transmission lines’ corridors and were
reported by an earlier study [10]. In that study, the statistical
distributions of sand grains size in the desert soil were acquired
from random samples, where their salinity and subsequent conductivity were measured. Based on the calculated influence of
sand grain size and salinity on the resulting leakage current, statistical distribution mapping was carried out to produce the
overall probability density distribution of leakage current.
The cumulative statistical distribution of leakage current was
then employed to assess the risk of insulator failure.
Methodology

M. El-Shahat and H. Anis


Fig. 1a
Table 1

Insulator shape with the shed as in ABB design guide.
Composite insulator dimensions.

Dimension

Symbol

Value (mm)

Inner diameter 1
Inner diameter 2
Length 1
Length 2
Length 3
Maximum length
Distance between two sheds
Height of long shed
Height of small shed

D1
D2
L1
L2
L3
Lmax
S

P
P1

250
219
680
855
470
2005
55
55
25

as shown in Fig. 1b. In ANSYS program, appropriate finiteelement meshes were then used for analysis, where the
potentials at the ends of the insulator
pffiffi were ground at one
end and the peak phase voltage 220pÃffiffi3 2 ¼ 179:629 kV at the
other side.
Sample insulator sector
It is both a tedious task and unnecessary to micro-analyze the
leakage current distribution along the entire insulator. Instead,
a sample sector of the insulator was selected, where the boundary conditions (local potential and electric field) resulting from
those conditions were placed around that sector. The insulator
sector has two sheds; one shed is long and the other is short
with a total creepage distance of 186.14 mm. The leakage current density materialized on the insulator surface as then
sought by means of ANSYS. Unigraphics was used to simulate
this sample insulator sector as shown in Fig 1c. The directional
components x and y of leakage current density were obtained,
from which the tangential (surface) current subsequently
resulted.

Results and discussion
Effect of contamination layer thickness

Insulator computational model
This paper uses a 220 kV ABB silicone rubber insulator as
shown in Fig. 1a; its dimensions are given in Table 1. The
UNIGRAPHICS program was used to create the insulator
model in 3-D and export it to the ANSYS program, where
the material of the insulator was defined to be silicone rubber,

The selected sample insulator simulation section of Fig. 1c was
subjected to the boundary conditions, where the potentials on
the two ends of the sample sector – as acquired from the global
analysis – were 54.196 kV and 49.828 kV.
Based on the statistical distributions of sand grain sizes in
Sinai – reported in an earlier study [10] – sand grains with
diameters in the range of 1–2 mm prevailed. Therefore, this


Risk assessment of desert pollution on composite high voltage insulators

Fig. 1b

Fig. 1c

Unigraphics 3-D model insulator.

Sample sector of composite insulator.

study takes this range of grain sizes and assumes that enough

accumulation creates a contamination layer of an equal thickness. Furthermore, chemical analysis carried out on acquired
samples determined the equivalent salt content (ESC, in mg
of salt/g of sand) of the pollution layer. It was observed that
a range of salinity of 0.5–1.5 mg salt/g sand was the most likely
to exist in Sinai.
To convert the salt content expressed in ESC (mg of salt/g
of sand) – as produced by the chemical analysis – into pollution layer electrical conductivity (S/m), the solution salinity
is first obtained from the expression [11]:
Sa ¼ 10À3 Â ESC Â Q

ð1Þ

Sa is the salinity of the solution. Q is the amount of sand
deposited on insulator surface with a certain amount of water.
Layer salinity is then related to electrical conductivity of
such solution is determined [12]:
Sa ¼ ð5:7 Â r20 Þ1:03

571

ð2Þ

r20 is the conductivity at a temperature of 20 °C in (S/m).
Using the theories of lattice geometry, the quantity Q can
be expressed as:


k
Âq
ð3Þ

Q¼
1Àk
where k is the lattice arrangement density, which is the proportion of the actual amount of particles (sand) that occupies a given space; q is the specific gravity of wet sand (1.92 g/ml).
The parameter k was calculated to fall in the range from
0.523 to 0.740 depending on the level of compactness [11].
The former value is much more realistic since sand will deposit
of the insulator surface in a rather loose fashion and it is,

therefore, not likely to deposit in an orderly space-optimized
manner. The lattice arrangement density k, in this work, is thus
chosen as 0.523.
The above values give a realistic Q value = 2.1 g/ml.
The above relations were applied over the reported range of
ESC to obtain the corresponding electrical conductivity. Table
2 shows the different conductivity of sand grain collected from
Sinai desert according to its ESC range using the value
Q = 2.1 g/ml.
These values were readily used in polluted insulator simulation in seeking the statistics of tangential electric field along
composite insulator, which drives the leakage current. The effects of those conductivities in each contamination layer on the
leakage current density on insulator surface were sought.
As an example, Fig. 2a shows the leakage current density
distribution over the creepage distance for a 1 mm contaminating layer thickness and with 284.9 lS/cm contaminant conductivity. By surface integrating current densities, the overall
surface leakage current was found to be 54.6 mA.
Figs. 2b–2d depict the effects on the surface distribution of
leakage current density of different conductivities in a 1, 1.5,
and 2 mm contamination layers, respectively. Surface integration was numerically performed to produce the surface leakage
currents in the above cases. The results are summarized in
Table 3.

Interdependence of leakage current on sand grain size and

conductivity
Leakage current intensities are seen to depend on changes in
the polluting sand’s salinity (and hence conductivity) and grain


572

M. El-Shahat and H. Anis
Conductivity of deposited wet sand layer estimation.

Equivalent
salt content (ESC)
(mg salt per g sand)

Salinity (Sa)
(mg/ml)

Conductivity
(r20) (lS/cm)

0.5
1.0
1.5

1.05
2.10
3.15

284.9
558.4

827.8

Leakage current density (A/m 2)

130

28.49 µs/cm
55.84 µs/cm
82.78 µs/cm

300

Leakage current density (A/m 2 )

Table 2

120

250

200

150

100

50

110


0

20

40

60

80

100

120

140

160

180

Creapage distance (mm)

100

Fig. 2c Leakage current density through 1.5 mm layer with
different conductivities.

90
80
70

60
50

0

20

40

60

80

100

120

140

160

180

Creapage distance (mm)

Fig. 2a Leakage current density near 1 mm contaminated layer
with 284.9 ls/cm conductivity.

size. Based on the above results, the relation between leakage
current and conductivity with different sand grain sizes, or

layer thickness, was numerically derived and is shown in
Fig. 3a. Similarly, the relation between leakage current and
grain size with different sand conductivities was produced
and is shown in Fig. 3b.
The joint dependence of leakage current on sand grain size
and on surface conductivity is the key to eventually deriving
the overall statistics of leakage current, on which the insulator’s failure risk assessment is based. This joint dependence
has been numerically derived using all available data and
results. Its general features are graphically seen in Fig. 3c.
284.9 µs/cm
558.4 µs/cm
827.8 µs/cm

Leakage current density (A/m2)

300

Fig. 2d Leakage current density through 2 mm layer with
different conductivities.

Table 3 Leakage current in mA for different layer thickness
and conductivity.
Layer thickness (mm)

250

1.0
1.5
2.0


200

Conductivity
284.9 lS/cm

558.4 lS/cm

827.8 lS/cm

54.60
56.23
58.93

96.00
98.34
115.5

140.87
145.78
171.22

150

Risk assessment of leakage current-based insulation failure
100

50
0

20


40

60

80

100

120

140

160

180

Creapage distance (mm)

Fig. 2b Leakage current density through 1 mm layer with
different conductivities.

Leakage current has been shown to depend on both the sand’s
contamination layer thickness and on its salinity and hence its
electrical conductivity. The above two variables were reported
to be random and may thus be expressed in statistical terms.
Subsequently, the leakage current can also be viewed as a random variable, whose probability density distribution is inevitably a product of the probability density distributions of the


Risk assessment of desert pollution on composite high voltage insulators


pollution layer conductivity and that of the pollution layer
thickness, which is – in turn – dictated by the sand grain size.
The two variables, conductivity c and sand grain size g, are
reasonably assumed to be statistically independent. If the
probability distributions of the conductivity and sand grain
size are, respectively, p(c) and p(g), then the probability distribution of leakage current p(I) would be

1600

Leakage current (mA)

1400
1200
1000
2.0 mm

800

PðIÞ ¼ PðcÞ Â PðgÞ

600

1.5 mm

400

0.5 mm

200

0

300

400

500

600

700

800

900

1000

Conductivity (µS/cm)

Fig. 3a Dependence of leakage current on conductivity, with
grain size as parameter.

Leakage current (mA)

150

558.4 µS/cm

100

420 µS/cm

50
284.9 µS/cm

0

573

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2


Fig. 3b Dependence of leakage current on grain size, with
conductivity as parameter.

1000
900

From the sand samples collected from regions in different
places in the desert, the frequency of occurrence distribution
of the equivalent salt content ESC (mg of salt/gm of sand)
could subsequently be built as shown in Fig. 4a. Fig. 4b subsequently shows the probability density distribution of the sand
conductivity p(c). In the following sections, statistical distributions were sought to describe the randomness of different variates (variables) relevant to this paper. In each case, a goodnessof-fit test was performed using MATLAB to select the statistical distribution that best fits the variable. A brief account of
the characteristics of each selected distribution is given in each
case.
Search was made for the standard probability function that
best fits the distribution of sand conductivity and was found to
be the Beta distribution. The Beta distribution is a family of
continuous probability distributions parameterized by two positive shape parameters, denoted by a and b, where the degree
of skewness is highly dependent on these parameters making
this distribution versatile and may accommodate various physical effects such as those seen with surface conductivity. It is,
therefore, very suitable for the case at hand. It is expressed by:
Pðc; a; bÞ ¼

Grain size (mm)

140 mA

ð4Þ

ða þ b À 1Þ! aÀ1

c ð1 À cÞbÀ1
ða À 1Þ!ðb À 1Þ!

ð5Þ

whose parameters are a = 3.0818 and b = 0.547; its mean is
298.7 lS/cm, and the standard deviation is 557.4 lS/cm with
a square error = 0.003504.
Fig. 4c shows the frequency distribution of sand in Sinai
and the associated probability density distribution of the sand
grain size p(g). Search was made for the standard probability
function that best fits that distribution and was found to be
the log-normal distribution. A log-normal distribution is a
continuous probability distribution of a random variable
whose logarithm is normally distributed. A variable might be
modeled as log-normal if it can be thought of as the multiplicative product of many independent random variables each of
which is positive. The distribution is always skewed toward

Conductivity (µS/cm)

800
700
600
100 mA

500
400
300

60 mA


200
100
0

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

Grain size (mm)

Fig. 3c Relation of conductivity to grain size, with leakage

current as parameter.

Fig. 4a

The frequency distribution of ESC of Sinai sand.


574

M. El-Shahat and H. Anis

Probability density function (1/µs/cm)

180
160
140
120
100
80
60
40
20
0

0

100

200


300

400

500

600

700

800

900

1000

Conductivity (µs/cm)

Fig. 4b
sand.

Probability density function of conductivity of Sinai

50
Probability density function
Grain size frequency

2

40


1.5

30

1

20

0.5

10

0

0
0

0.5
0.5

1
1

1.5
1.5

2
2


2.5
2.5

3
3

Frequency

Probability density function (1/mm)

2.5

0

Grain size (mm)

Fig. 4c

Probability density function of grain sizes in all Sinai.

and over, each time using a different set of random values from
the probability functions. Depending upon the number of
uncertainties and the ranges specified for them, a Monte Carlo
simulation could involve thousands or tens of thousands of
recalculations before it is complete. Monte Carlo simulation
produces distributions of possible outcome values. By using
probability distributions, variables can have different probabilities of different outcomes occurring. It is emphasized in this
paper that probability distributions are a much more realistic
way of describing uncertainty in variables of a risk analysis.
This procedure is diagrammatically described in Fig. 5.

Random numbers Rgi and Rci were first numerically generated.
Random values of contamination layer conductivity (ci) and
layer size (gi) were in turn generated. Random magnitudes of
leakage current (Ii) using the two random ci and gi values were
then generated using the numerical techniques described in this
paper.
Using large enough generated sample of Ii values, the overall probability density distribution of leakage current was produced and is shown in Fig. 6a. Search was made for the
standard probability function that best fits that distribution
and was found to be the Weibull distribution. The Weibull distribution has the ability to assume the characteristics of many
different types of distributions. This has made it extremely
popular among engineers and quality practitioners, who have
made it the most commonly used distribution for modeling
reliability data. It is flexible enough to model a variety of data
sets, and having displayed the best fit to the present case study,
it has been adopted. It is expressed by:
k xkÀ1 ÀðxkÞk
Pðx; k; kÞ ¼
e
; x>0
ð7Þ
k k
whose parameters are k = 49.7 and k = 0 0.344; its mean is
67.5 mA, and the standard deviation is 21 mA with a square
error = 0.018915.
The above leakage current, whose mean value is 67.5 mA,
describes the actual expected leakage current for this particular
case study, i.e., the specified insulator with those prevailing
pollution conditions mentioned in the paper. Other insulators
under different conditions would produce other statistics.


lower values as it is in the case study, where the degree of skewness increases as the relative standard deviation increases. It is
expressed by:
Pðx; l; rÞ ¼

ðln xÀlÞ2
1
pffiffiffiffiffiffi eÀ 2r2 ;
x à r 2p

x>0

ð6Þ

whose mean is 0.401 mm, and the standard deviation is
0.346 mm with a square Error = 0.110271.
Deriving the leakage current probability distribution
Since – based on the above results – no analytical formulation
for the resultant leakage current probability density distribution p(I) could be derived, an alternative way was to use the
Monte Carlo technique. Monte Carlo simulation is a computerized mathematical technique that permits accounting for risk
in quantitative analysis and decision making. It performs risk
analysis by building models of possible results by substituting
a range of values – a probability distribution – for any factor
that has inherent uncertainty. It then calculates results over

Fig. 5 Computation of leakage current statistics by Monte Carlo
technique.


Risk assessment of desert pollution on composite high voltage insulators


hence, it also indicates the chances for insulator failure to occur. Fig. 6b displays the final result of the present case study.
For the given insulator, placed in the presently defined environment, and under the given power line voltage (220 kV), the figure gives – for any arbitrarily set value of critical leakage
current – the risk of having an insulator failure under desert
pollution conditions. For example, a set critical leakage current
magnitude of 100 mA reflects a 60% chance of insulator failure.

Probability density function (1/mA)

0.08
0.07
0.06
0.05
0.04
0.03

Conclusions

0.02
0.01
0

0

10

20

30

40


50

60

70

80

90

100

Leakage current (mA)

Fig. 6a

Probability density function of leakage current.

0.8

0.7

Risk estimate

575

0.6

0.5


0.4

1. Under conditions of desert pollution and wetness, the leakage current density along the contaminated layer on composite insulator for a given contaminant layer thickness
and salinity (hence, conductivity) was computed and subsequently produced the total leakage current magnitude.
2. The interrelationships between grain size, conductivity, and
leakage current were estimated. The statistics of surface
leakage current that depend on the probability distribution
for those two independent variables (conductivity and grain
size) was produced using a Monte Carlo technique. The
log-normal distribution was found to best fit the leakage
current statistical distribution, with mean value of
6.75 mA and standard deviation 2.1 mA in the present
study case.
3. A novel method is given to estimate the risk of flashover
under pollution, where the cumulative probability density
of the leakage current is used in this work as a direct tool
for the risk of insulation failure.

0.3

0.2

0

50

100

150


200

250

300

Leakage current (mA)

Fig. 6b

Conflict of interest
The authors have declared no conflict of interest.

Risk estimation of insulator failure.

Compliance with Ethics Requirements
However, it is advisable for the electric power utility to assess
the danger of a leakage-current-based insulator breakdown in
a probabilistic –rather than deterministic – way. In other ways,
the degree of uncertainty in predicting a flashover is to be estimated. In this case, reliance is not on the estimated mean leakage current (67.5 mA) but rather on its statistical distribution.
The mean current is, therefore, not particularly marked in
Figs. 6a and 6b since the distribution of risk is of value.
Risk failure calculation
Research has consistently shown that the magnitude of leakage
current is a reliable predictor of insulator surface discharge
and the ultimate insulator failure. Therefore, the probability
distribution of leakage current can be used to assess the risk
of insulator failure.
Based on the probability density distribution, the cumulative probability of the leakage current can be produced.

A critical magnitude of leakage current may be set by the
electricity utility as that, beyond which insulator failure is eminent. The cumulative probability function then indicates the
chances for that set leakage current value to be exceeded, and

This article does not contain any studies with human or animal
subjects.
References
[1] Sokolijia K, Kapetanovic M, Hajro M. Some considerations
concerning composite insulators design. Eleco’99 international
conference on electrical and, electronic engineering. E02.02/A601; December 1999.
[2] Goudie J. Silicone rubber for electrical insulators; 1998.
< />rubber_tech98.pdf>.
[3] Zhang H, Hackam R. Surface resistance and hydrophobicity of
HTV silicone rubber in the presence of salt-fog. Conference
record of the 1998 IEEE international symposium on electrical
insulation, vol. 2; June 1998. p. 355–9.
[4] Zhu Y, Haji K, Yamamoto H, Miyake T, Otsubo M, Honda C,
et al. Distribution of leakage current on polluted polymer
insulator surface. Conference on electrical insulation and
dielectric phenomena; 2006.
[5] Ahmed A, Singer H, Mukherjee P. A numerical model using
surface charges for the calculation of electric fields and leakage
currents on polluted insulator surfaces. In: IEEE conference on


576

[6]

[7]


[8]

[9]

M. El-Shahat and H. Anis
electrical insulation and dielectric phenomena, Annual Report,
vol. 1; 1998.
Zhicheng G, Guoshun C. A study on the leakage current along
the Surface of Polluted Insulator. In: Proceedings 4th
international conference on properties and applications of
dielectric materials; July 3–8, 1994.
Arafa A, Nosseir A. Effect of severe sandstorms on the
performance of polymeric insulators. CIGRE, F-75008 Paris,
D1–104; 2012.
Hamza H, Abdelgawad N, Arafa B. Effect of desert
environmental conditions on the flashover voltage of
insulators. Energy Convers Manage 2002;43(17):2437–42.
El-Hag A, Jayaram S, Cherney E. Calculation of current density
along insulator surface using field and circuit theory approaches.
Annual report conference on electrical insulation and dielectric
phenomena; 2003.

[10] Mahdy M, Anis H, Amer R, El-Morshedy A. Insulator
pollution assessment in Sinai using geographic information
systems. In: Proceedings of the middle east power conference
(Mepcon 2001); December 2001.
[11] Henry C, Abhinav K. The densest lattice in twenty-four
dimensions. Electronic Res Announ Am Math Soc
2004;10(07):58–67.

[12] Salam M, Nadir Z, Mohammad N, Al Maqrashi A, Al
Kaf A, Al Shibli T, et al. Measurement of conductivity
and equivalent salt deposit density of contaminated glass
plate. TENCON IEEE region 10 conference; November
2004.